document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=224164>Question 224164</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The wind is blowing at a steady rate of 10 mph.  It takes a truck a total of 5 hours to travel 120 miles west against the wind and then 120 miles back with the wind.  What is the trucks speed in still air? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #167477 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=167477\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The wind is blowing at a steady rate of 10 mph. It takes a truck a total of 5 hours to travel 120 miles west against the wind and then 120 miles back with the wind. What is the trucks speed in stil<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Applying the distance formula: d = rt<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Let x = speed of truck in still wind<BR>\n" );
document.write( "and y = time traveling against the wind<BR>\n" );
document.write( "then<BR>\n" );
document.write( "\"distance traveling against wind\"<BR>\n" );
document.write( "(x-10)y = 120<BR>\n" );
document.write( "\"distance traveling with wind\"<BR>\n" );
document.write( "(x+10)(10-y) =120<BR>\n" );
document.write( ".<BR>\n" );
document.write( "So, now we have two equations and two unknowns:<BR>\n" );
document.write( "(x-10)y = 120  <BR>\n" );
document.write( "(x+10)(10-y) =120<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Our system of equations:<BR>\n" );
document.write( "(x-10)y = 120  (equation 1)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "(x+10)(10-y) =120<BR>\n" );
document.write( "10x-xy-10y+100 = 120 (equation 2)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Solve equation 1 for y:<BR>\n" );
document.write( "y = 120/(x-10)<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Plug the definition of y (above) into equation 2 and solve for x:<BR>\n" );
document.write( "10x-xy-10y+100 = 120<BR>\n" );
document.write( "10x+100-xy-10y = 120<BR>\n" );
document.write( "10x+100-(xy+10y) = 120<BR>\n" );
document.write( "10x+100-y(x+10) = 120<BR>\n" );
document.write( "10x+100-(120/(x-10))(x+10) = 120<BR>\n" );
document.write( "Multiply BOTH sides by (x-10) to get rid of denominators:<BR>\n" );
document.write( "10x(x-10)+100(x-10)-120(x+10) = 120(x-10)<BR>\n" );
document.write( "10x^2-100x+100x-1000-120x-1200 = 120x-1200<BR>\n" );
document.write( "10x^2-120x-2200 = 120x-1200<BR>\n" );
document.write( "10x^2-240x-1000 = 0<BR>\n" );
document.write( "x^2-24x-100 = 0<BR>\n" );
document.write( "Since we can't factor, we must resort to the quadratic equation.  Doing so will yield:<BR>\n" );
document.write( "x = {27.62, -3.62}<BR>\n" );
document.write( "A negative speed does NOT make sense, so toss it out leaving:<BR>\n" );
document.write( "x = 27.62 mph<BR>\n" );
document.write( ".<BR>\n" );
document.write( "Details of quadratic equation to follow:<BR>\n" );
document.write( "<TABLE  BORDER=1>\n" );
document.write( "\n" );
document.write( " <TR><TD  ALIGN=MIDDLE>Solved by <A  rel=nofollow HREF=http://wiki.algebra.com/index.php/Tutoring_-_pluggable_solvers>pluggable</A> solver: <A  rel=nofollow HREF=quadratic.solver>SOLVE quadratic equation with variable</A></TD></TR>\n" );
document.write( "<TR><TD  ALIGN=LEFT>Quadratic equation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ax%5E2%2Bbx%2Bc=0 ALIGN=MIDDLE  ALT=\"ax%5E2%2Bbx%2Bc=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > (in our case <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-24x%2B-100+=+0 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-24x%2B-100+=+0\"   DISABLED_style= \"max-width:90%; height:auto;\" >) has the following solutons:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  <BR>\n" );
document.write( "  For these solutions to exist, the <U>discriminant</U> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" > should not be a negative number.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  First, we need to compute the discriminant <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac ALIGN=MIDDLE  ALT=\"b%5E2-4ac\"   DISABLED_style= \"max-width:90%; height:auto;\" >: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2-4ac=%28-24%29%5E2-4%2A1%2A-100=976 ALIGN=MIDDLE  ALT=\"b%5E2-4ac=%28-24%29%5E2-4%2A1%2A-100=976\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "  Discriminant d=976 is greater than zero. That means that there are two solutions: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+x%5B12%5D+=+%28--24%2B-sqrt%28+976+%29%29%2F2%5Ca ALIGN=MIDDLE  ALT=\"+x%5B12%5D+=+%28--24%2B-sqrt%28+976+%29%29%2F2%5Ca\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "  <BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B1%5D+=+%28-%28-24%29%2Bsqrt%28+976+%29%29%2F2%5C1+=+27.6204993518133 ALIGN=MIDDLE  ALT=\"x%5B1%5D+=+%28-%28-24%29%2Bsqrt%28+976+%29%29%2F2%5C1+=+27.6204993518133\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5B2%5D+=+%28-%28-24%29-sqrt%28+976+%29%29%2F2%5C1+=+-3.62049935181331 ALIGN=MIDDLE  ALT=\"x%5B2%5D+=+%28-%28-24%29-sqrt%28+976+%29%29%2F2%5C1+=+-3.62049935181331\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "    <BR>\n" );
document.write( "    Quadratic expression <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-24x%2B-100 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-24x%2B-100\"   DISABLED_style= \"max-width:90%; height:auto;\" > can be factored:<BR>\n" );
document.write( "  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1x%5E2%2B-24x%2B-100+=+1%28x-27.6204993518133%29%2A%28x--3.62049935181331%29 ALIGN=MIDDLE  ALT=\"1x%5E2%2B-24x%2B-100+=+1%28x-27.6204993518133%29%2A%28x--3.62049935181331%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "  Again, the answer is: 27.6204993518133, -3.62049935181331.\n" );
document.write( "Here's your graph:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-24%2Ax%2B-100+%29 ALIGN=MIDDLE  ALT=\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-24%2Ax%2B-100+%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ></TD></TR>\n" );
document.write( "</TABLE><BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );